Related papers: The extremal plurisubharmonic function of the toru…
We correct the calculation of the Monge-Amp\`ere measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.
In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic functions.
In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
We find polyhedral divisors corresponding to the torus action of complexity one on affine trinomial hypersurfaces. Explicit computations for particular classes of such hypersurfaces including Pham-Brieskorn surfaces and rational trinomial…
We give a qualitative description of extremals for Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by extremals and the observation that extremals are optimal for a…
Let $X$ be a compact K\"ahler manifold and $\theta$ a smooth closed $(1,1)$-real form representing a big cohomology class $\alpha \in H^{1,1}(X,\R)$. The purpose of this note is to show, using pluripotential and viscosity techniques, that…
We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our theory extends classical cone constructions of…
We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.
We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that $f$ is a measurable, real-valued, Lipschitz function on the torus $\mathbb{T}^{\infty}$. We prove that there exists a number $a \in…
The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n
We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler…
In this work we use the method of eigenfamilies to construct explicit complex-valued proper $p$-harmonic functions on the compact real Grassmannians. We also find proper $p$-harmonic functions on the real flag manifolds which do not descend…
We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.
We show that a natural complexification and a mild generalization of the idea of completeness guarantee geodesic completeness of Clifton-Pohl torus; we explicitely compute all of its geodesics.
This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants,…
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
We show that the physical states of a 10 dimensional superstring moving on a torus form a generalized Kac-Moody superalgebra. This gives the first explicit realizations of these algebras. For a special torus the denominator function of this…
In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half,…
We establish faithful tropicalisation for point configurations on algebraic tori. Building on ideas from enumerative geometry, we introduce tropical scaffolds and use them to construct a system of modular fan structures on the tropical…